How can I take back my sovereignty from the American government and start my own micro nation?
I've read about starting a foreign company with my name in all caps but I want a lawyer's answer.
You are courting seduction by the sovereign citizen doctrine. This is a crackpot legal theory that will get you nowhere. Run away as fast as you can.
See, for example, Can a natural US person hold citizenship while remaining non-juridical?.
See also "Mercedes-Benz Financial (DCFS Canada Corp.) v. Kovacevic, 2009", CanLII. This person fared particularly poorly because his argument relied in part on the UCC, which is a United States model code, but he was arguing in a Canadian court.
Still, even in a US court, he would have lost. See What are "freemen of the land" or "sovereign citizen" theories and do they hold any water?.
Unfortunately for you, as long as you remain physically inside the borders of the United States you will be subject to the jurisdiction of the laws of the United States and whatever other state, county, city or town (each with its own separate body of law) you are also located at the time. (FYI: This multi-level jurisdictional framework is called federalism and is rooted in the founding of the United States and the creation of the U.S. Constitution).
I think your best option is to explore the possibility of renouncing your American citizenship and explore relocating to somewhere like the Pitcairn Islands (in the South Pacific). Last I read, they were giving away free land in an effort to populate the island. There are only about 50 people living there so you might be able to work out a deal.
With a population of only around fifty, the people of Pitcairn are descended from the mutineers of HMAV Bounty and their Tahitian companions. Pitcairn Island is approximately 3.2km (2 miles) long and 1.6km (1 mile) wide with the capital Adamstown located above Bounty Bay and accessed by the aptly named road, "The Hill of Difficulty".
They are apparently still a British Colony and, therefore, subject to British Law. But there is a United Nations Special Committee on Decolonization that might be helpful in obtaining independence.
FYI, the tale of the mutiny of the Bounty has been retold countless times and offers an intriguing and unique backstory to the origin and founding of the nation of Pitcairn.
You simply claim whatever you want. Getting other sovereigns to acknowledge your legitimacy is a more difficult problem. The solution is typically to gather followers, amass armies and enforce your claim as required. The US succeeded in this in the Revolutionary war. The Confederate States ultimately failed in the U.S. civil war. But the idea is the same.
You could have a chat with 'Prince' Michael Bates of the Principality of Sealand. In September 1967 his father, 'Prince' Roy Bates, did something similar to what you appear to have in mind.
In international law, the most common schools of thought for the creation of statehood are the constitutive and declaratory theories of state creation. The constitutive theory is the standard nineteenth-century model of statehood, and the declaratory theory was developed in the twentieth century to address shortcomings of the constitutive theory. In the constitutive theory, a state exists exclusively via recognition by other states. The theory splits on whether this recognition requires 'diplomatic recognition' or merely 'recognition of existence'. No other state grants Sealand official recognition, but it has been argued by Bates that negotiations carried out by Germany following a brief hostage incident constituted 'recognition of existence' (and, since the German government reportedly sent an ambassador to the tower, diplomatic recognition). In the declaratory theory of statehood, an entity becomes a state as soon as it meets the minimal criteria for statehood. Therefore, recognition by other states is purely 'declaratory'
If you can make any real sense of the above quote then you are a more dedicated man than I. As far as I can tell, the general idea is that if you can find (or construct) any land that is not already claimed, you may claim it. But whether or not your independent 'nation state' is recognised by others is discretionary. Even without recognition, at that point, you're probably in a position to avoid being under the duress of your birth nation so long as you don't physically reside there.
While I wholeheartedly agree with others who have said "you can't", and it is practically true, and the "All Caps" thing is definately BS, you can, theoretically start your own Micro-nation. The difficulties will be finding a place which is not governed and getting recognition of other nations.
If you want sovereignity over a piece of land, then you would need to figure out how to handle anyone else who claims sovereignity over it. The government of USA is currently claiming sovereignity over all its territory and (as far as I know) is not willing to negotiate over it. As long as you are on USA soil, they are free to ignore any declarations, assert their claim of sovereignity, and enforce their laws on you without your consent. The answer to "How can I take back my sovereignty from the American government?" is "make them", and forcibly making the USA government to do that is left as an exercise for the reader.
You may have better success claiming sovereignity somewhere else, there are territories worldwide that are less interesting to others and where your claim of sovereignity is less likely to be contested.
Not only will you need to find unclaimed land (unless you want to wage war); you may also have trouble renouncing your US citizenship. I was sure that the government can refuse to let you go until you pay all owed tax; but all proof I could find for that was a non-official web site claiming that "if a court determines that you are expatriating to avoid paying a tax or taxes, they can force you to stay against your will".
But it is official that by renouncing your citizenship you give up all privileges while you retain many duties towards the government or other citizens. Among others you will still be subject to criminal prosecution and military service and be forced to pay owed tax and child support.
You can try, but prepare to face the consequences.
The "only" thing you need is to be acknowledged by other countries. Having the support of at least one of superpowers, territory and population is often not enough - see Taiwan, Somaliland, Kosovo, South Osetia...
There's no unclaimed continental territory. Everything is either claimed or proclaimed the international, free territory (Antarctica). So you'll need to claim the rights to some part of other country (see Crimea). You'll be almost surely proclaimed terrorist and fighted to death, so make sure you have enough manpower and weapons and international support before you can do. If you can find some success stories other than Crimea and Kosovo, see the history of Texas. They first colonize a part of Mexico territory, then (with support of United States) proclaimed independence (to finally end up as one of the US states).
You could claim some uninhabited islands, but it won't be anyway easier. As an independent nations, you have, by international maritime law, claims to exclusively use the maritime territory around your new state, which would otherwise be international territory of all nations. Don't expect them to appreciate that fact, with the exception of the nation you choose to be your patron, and give her the rights to exploit "your" territory for the protection. And don't be surprised if you get bombarded in some unfortunate accident during "maneuvers" on the "international" territory. See Spratly Islands to see how serious the things can be.
The easiest way would be to simply buy a part of some other country's territory, maybe some almost uninhabited part of Siberia? Or Canada? A few (hundred) billion dollar should be enough. As long as your new country is useful (as tax paradise for the richest, for example), this deal might even be respected in the future.
Or maybe you could finance the expedition to the Mars, and buy a permanent space base there. The international law considers all the space as the international territory, which cannot be claimed by any state, however, international law change, so once the other nations acknowledge the sovereignty of your newly formed state, so will be it. You'll need a bit more than a funny few billion dollar to achieve that, though. But the option is open.